The necessity of dealing with uncertainty in real world problems has been a long‐term research challenge that has originated different methodologies and theories. Fuzzy sets along with their extensions, such as type‐2 fuzzy sets, interval‐valued fuzzy sets, and Atanassov's intuitionistic fuzzy sets, have provided a wide range of tools that are able to deal with uncertainty in different types of problems. Recently, a new extension of fuzzy sets so‐called hesitant fuzzy sets has been introduced to deal with hesitant situations, which were not well managed by the previous tools. Hesitant fuzzy sets have attracted very quickly the attention of many researchers that have proposed diverse extensions, several types of operators to compute with such types of information, and eventually some applications have been developed. Because of such a growth, this paper presents an overview on hesitant fuzzy sets with the aim of providing a clear perspective on the different concepts, tools and trends related to this extension of fuzzy sets.